Amin H. Almasri George Z. Voyiadjis e-mail: voyiadjis@eng.lsu.edu Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803 Effect of Strain Rate on the Dynamic Hardness in Metals Traditionally, the hardness of materials is determined from indentation tests at low load- ing rates (static). However, considerably less work has been conducted in studying the dynamic hardness of materials using relatively high loading rates. In the present work, two models are used to predict strain rate dependency in hardness. The first model is a power law expression that is based on the dependence of the yield stress on the strain rate. This model is relatively simple in implementation, and it is quite easy to determine its parameters from simple uniaxial experiments. The second model is a micromechanical based model using Taylor’s hardening law. It utilizes the behavior of dislocation densities at high strain rates in metals in order to relate dynamic hardness to strain rates. The latter model also accounts for any changes in temperature that could exist. A finite element is also run and compared with the two models proposed in this work. Results from both models are compared with available experimental results for oxygen-free high- conductivity copper and 1018 cold rolled steel, and both models show reasonably good agreement with the experimental results. DOI: 10.1115/1.2744430 Keywords: dynamic hardness, strain rate, metals Introduction Indentation tests in metals are usually used to measure one of the most basic material characteristics, which is the hardness of the material. Indentation tests can be described simply as forcing a hard indenter spherical ball, cone, or pyramid into a relatively softer material and the load on the indenter is measured versus the indentation depth. Although the simplicity of the indentation ex- periment has made it a very common test, the indentation process includes some complicated phenomena, such as plastic behavior, friction at the interface, and the fact that the indentation problem is primarily a three-dimensional problem. One of the most impor- tant factors that affect the indentation process is the strain rate effect, which will be investigated in the present work. Hardness obtained through low rates of loading, termed “static hardness” in this work, has been studied extensively for a long time both experimentally and theoretically through different theo- ries and approaches. However, less work has been carried out studying the hardness behavior for strain-dependent material un- der high strain rate of loading. Tabor 1 defined the dynamic hardness as the resistance of the metal to local indentation when the indentation is produced by a rapidly moving indenter. He dis- cussed dynamic hardness due mainly to a falling indenter under gravity on the metal surface and defined the dynamic hardness as the energy of impact over the volume of indentation. Researchers found that the volume of indentation is directly proportional to the kinetic energy of the indenter, which implies that the metal offers an average pressure of resistance to the indenter. In a different approach, the energy of rebound was taken as a measure of dy- namic hardness. Regardless of the method used to measure the dynamic hardness, it was found that dynamic hardness is always higher than static or quasi-static hardness, or in other words, hard- ness value increases with increasing applied load rate or generally with increasing strain rate of loading. Due to damage in structures subjected by blasts and impact loads there has been considerable recent interest by researchers in determining the dynamic hardness in materials and the effect of strain rate on it. Koeppel and Subhash 2 used an experimental machine setup that utilizes the elastic stress wave propagation phenomena in a slender rod to determine the dynamic Vickers indentation hardness in metals. The results were verified by ob- taining the constitutive response of materials at similar strain rates and then correlating the yield stress with the corresponding hard- ness. The characteristics of the induced plastic zone under static and dynamic indentations were investigated by contouring micro- indentation hardness measurements of the indented regions. The results showed that the size of the plastic zone highly depends on yield stress under static and dynamic conditions. Anton and Sub- hash 3 performed static and dynamic Vickers indentations on six different brittle materials to study the rate effects in hardness and fracture toughness. The dynamic indentations were performed on the same aforementioned hardness tester that is based on elastic stress wave propagation phenomena. Under dynamic indentations, an increase in hardness was observed in all the brittle materials compared to their static hardness measurements. Lu et al. 4 developed a dynamic indentation technique to mea- sure time-resolved depth and load responses during the process of indentation. A moiré interferometry-based displacement measure- ment technique was utilized to measure the depth of indentation and a quartz load transducer was used to measure the load. They introduced a new methodology to deduce the dynamic rate sensi- tivity of materials using the measured data. Andrews et al. 5 investigated the impact of a sharp indenter at low impact veloci- ties for elastoplastic materials. They developed a one-dimensional model based on the assumption that under dynamic conditions—as well as under static conditions—the variation of indentation load is a parabolic function of the depth Kick’s law. The motion of the indenter as it indents and rebounds from the target was investigated. For rate-independent materials agreement with the model was good provided the impact velocity did not exceed certain critical values. For rate-dependent materials, the relationship between load and depth in the impact problem is no longer parabolic and the model predictions cannot be applied to this case. It was suggested that the rate-dependent case can be solved by incorporating the relationship between the motion of the indenter and the dynamic flow properties of the material into the equation of motion for the indenter. Initially Voyiadjis and Buck- ner 6 and Voyiadjis et al. 7 studied the axisymmetric contact problem for the elasto-plastic behavior of materials subjected to spherical static indentation using the finite element method with mixed boundary conditions. Vasauskas 8 divided the complete Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received August 24, 2006; fi- nal manuscript received April 9, 2007. Review conducted by Mark F. Horstemeyer. Journal of Engineering Materials and Technology OCTOBER 2007, Vol. 129 / 505 Copyright © 2007 by ASME Downloaded 26 Oct 2007 to 132.170.201.36. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm